Two dimensional dipolar coupling in monolayers of silver and gold nanoparticles on a dielectric substrate.

The dimensionality of assembled nanoparticles plays an important role in their optical and magnetic properties, via dipolar effects and the interaction with their environment. In this work we develop a methodology for distinguishing between two (2D) and three (3D) dimensional collective interactions on the surface plasmon resonance of assembled metal nanoparticles. Towards that goal, we elaborate different sets of Au and Ag nanoparticles as suspensions, random 3D arrangements and well organized 2D arrays. Then we model their scattering cross-section using effective field methods in dimension n, including interparticle as well as particle-substrate dipolar interactions. For this modelling, two effective field medium approaches are employed, taking into account the filling factors of the assemblies. Our results are important for realizing photonic amplifier devices.